Matrix Operations Underlying the Transformer Models

Session

Computer Science and Communication Engineering

Description

This paper explores the mathematical principles underlying the transformer model, an architecture that is driving the advancement of artificial intelligence (AI). While older processing models like Recurrent Neural Networks and Long Short-Term Memory Networks struggled with long range dependencies and parallel computations, transformers overcome these challenges through self attention and parallelism. The core of this architecture lies matrix operations, specifically matrix multiplication and the dot product, which allow transformers to capture relationships across sequences.This paper first walks us through the traditional sequential models, then outlines the encoder, decoder and encoder-decoder variations that define the modern transformer architecture. We then focus on Query, Key and Value matrices within the attention mechanism, and illustrating the computation of attention using embedding vectors and weight matrices through a concrete example.By focusing on the linear algebra underlying transformer models, this paper shows how mathematical operations ensure efficiency and performance in natural language processing (NLP) and beyond. Understanding these fundamental mathematical principles clarifies how transformers work and provides insight into the future of AI.

Keywords:

Artificial Intelligence, Decoder, Dot Product, Encoder, Long Short-Term Memory Networks (LSTMs), Matrix, Matrix Multiplication, Natural Language Processing (NLP), Recurrent Neural Networks (RNNs), Self Attention, Transformer

Proceedings Editor

Edmond Hajrizi

ISBN

978-9951-982-41-2

Location

UBT Kampus, Lipjan

Start Date

25-10-2025 9:00 AM

End Date

26-10-2025 6:00 PM

DOI

10.33107/ubt-ic.2025.84

This document is currently not available here.

Share

COinS
 
Oct 25th, 9:00 AM Oct 26th, 6:00 PM

Matrix Operations Underlying the Transformer Models

UBT Kampus, Lipjan

This paper explores the mathematical principles underlying the transformer model, an architecture that is driving the advancement of artificial intelligence (AI). While older processing models like Recurrent Neural Networks and Long Short-Term Memory Networks struggled with long range dependencies and parallel computations, transformers overcome these challenges through self attention and parallelism. The core of this architecture lies matrix operations, specifically matrix multiplication and the dot product, which allow transformers to capture relationships across sequences.This paper first walks us through the traditional sequential models, then outlines the encoder, decoder and encoder-decoder variations that define the modern transformer architecture. We then focus on Query, Key and Value matrices within the attention mechanism, and illustrating the computation of attention using embedding vectors and weight matrices through a concrete example.By focusing on the linear algebra underlying transformer models, this paper shows how mathematical operations ensure efficiency and performance in natural language processing (NLP) and beyond. Understanding these fundamental mathematical principles clarifies how transformers work and provides insight into the future of AI.